Nonreflective coating

ABSTRACT

A nonreflective coating is made up of five or seven layers of optical films provided on an optical element, such as a lens, whose refractive index is in a certain refractive index range for a particular light wavelength. The layers are formed of two materials different in refractive index so that the odd layers have one of the two refractive indexes while the even layers have the other refractive index, and the thicknesses of the layers are suitably defined as functions of the light wavelength.

This is a continuation of application Ser. No. 752,000, filed Dec. 17,1976 and now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to nonreflective coatings, and more particularlyto nonreflective coatings applied to optical elements such as lenses.

A nonreflective coating based on the interference of equal inclinationis well known in the art, and such a nonreflective coating is applied tooptical elements such as lenses (hereinafter referred to as "opticalsubstrates" or simply "substrates" when applicable). The nonreflectivecoating of this type comprises three layers of optical films, or simplyfilms (as in U.S. Pat. No. 3,185,020, and Japanese Patent PublicationNo. 28821/1975), and is disadvantageous in the following points.

(1) It is necessary to provide three different films which have high,middle, and low refractive indexes, respectively, on a substrate, and(2) furthermore it is necessary to change the refractive indexes of thethree films, especially the refractive index of the film with the middlerefractive index if the refractive index of the substrate is changed.The number in kind of materials which can satisfy these requirements isof the order of three if the reproducibility thereof is taken intoconsideration.

(3) The films are deposited, for instance, by vacuum evaporation. Inthis case, the film thus deposited is liable to be nonuniform inrefractive index, and accordingly the reflection preventing effectthereof for the central part of the visible ray range is greatlydeviated from the design value.

(4) It is very important in the field of photographical technique thatsuch films show high transmissivity with respect to light in the nearultraviolet ray range. However, due to the above-describednonuniformity, a film made of a certain material may absorb a large partof the near ultraviolet rays at its thick portion.

In addition, (5) in order to eliminate the above-describednonuniformity, a method has been proposed in which gas such as oxygen orair is employed in depositing the films by vacuum evaporation. However,this method is disadvantageous in that the film formed thereby isinsufficient in strength.

SUMMARY OF THE INVENTION

Accordingly, an object of this invention is to provide a nonreflectivecoating in which all of the above-described difficulties accompanying aconventional nonreflective coating have been eliminated.

More specifically, an object of the invention is to provide anonreflective coating which is made of a relatively small number ofmaterials different in refractive index and is applicable to a substratewhose refractive index is in a relatively wide refractive index range,showing an excellent reflection preventing effect over a wide range oflight wavelength.

The novel features believed characteristic of this invention are setforth in the appended claims. This invention itself, however, as well asother objects and advantages thereof may best be understood by referenceto the following detailed description of illustrative embodiments, whenread in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is an explanatory diagram illustrating a first embodiment of anonreflective coating according to this invention;

FIGS. 2 through 8 are graphical representations indicating thereflection preventing effects of various concrete examples according tothe first embodiment shown in FIG. 1;

FIG. 9 is an explanatory diagram illustrating a second embodiment of thenonreflective coating according to the invention; and

FIGS. 10 through 16 are graphical representations indicating thereflection preventing effects of various concrete examples according tothe second embodiment shown in FIG. 9.

DETAILED DESCRIPTION OF THE INVENTION

In order to eliminate the above-described difficulties (1) and (2)accompanying the conventional non-reflective coating made up of threelayers of optical films, a first embodiment of a non-reflective coatingaccording to this invention, as shown in FIG. 1, comprises five layersof films L₁ through L₅ which are formed on an optical substrate L_(b)such as a lens in the order opposite to the stated order. Morespecifically, the first film L₁ has a surface exposed to the surroundingatmosphere SA, while the fifth film L₅ is deposited directly on thesubstrate L_(b), and the remaining films L₂, L₃ and L₄ are disposedbetween the first and fifth films L₁ and L₅. In FIG. 1, the refractiveindexes of the films L₁ through L₅ and the substrate L_(b) aredesignated by n₁, n₂, n₃, n₄, n₅ and n_(b5), respectively.

The films L₁ through L₅ are formed of two materials different inrefractive index. More specifically, the odd numbered films, i.e. thefirst, third and fifth films L₁, L₃ and L₅ are made of a material havinga low refractive index such as magnesium fluoride MgF₂ whose refractiveindex is 1.39.

In this case, the films L₁, L₃ and L₅ are effective when the opticalthicknesses d₁, d₃ and d₅ thereof satisfy the following limitations:##EQU1## where λ_(o) is the light wavelength.

It should be noted that the optical thickness of the film L₅ depositedon the substrate L_(b) is determined from the refractive index n_(b5) ofthe material of the substrate L_(b).

On the other hand, the second and fourth films L₂ and L₄ are made of amaterial having a high refractive index such as zirconium oxide ZrO₂,titanium oxide TiO₂, or cerium oxide CeO₂. In this case, similarly as inthe above-described case, the films L₂ and L₄ are effective when theoptical thicknesses d₂ and d₄ thereof satisfy the following limitations:##EQU2##

d₂ is substantially equal to d₄.

Optical thickness calculations are carried out by the Herpin matrixmethod which is described in U.S. Pat. No. 3,799,653 at columns 5-7 ofthe patent. The Herpin matrix method is also described in the book"Thin-Film Optical Filters" by H. A. Macleod, Adam Hilger Ltd., London.

According to the concerned experiments, it is especially preferable inthe case of five layers of operating films that the refractive indexn_(b5) of the substrate L_(b) is in the range of from 1.65 to 1.90 i.e.1.65≦n_(b5) ≦1.90.

The relationships between the film thicknesses and the refractiveindexes described above will be further described by reference toconcrete examples in which the above-described wavelength λ_(o) isemployed.

EXAMPLE 1-1

When on a substrate L_(b) having a refractive index n_(b5) =1.65 weredeposited five layers of films L₁ -L₅ made of two different materials sothat the refractive indexes n₁, n₂, n₃, n₄ and n₅ thereof arerespectively 1.39, 2.00, 1.39, 2.00 and 1.39 and that the opticalthicknesses d₁, d₂, d₃, d₄ and d₅ thereof are respectively 0.270 λ_(o),0.210 λ_(o), 0.055 λ_(o), 0.173 λ_(o) and 0.037 λ_(o), the variation ofreflectivity R(%) with wavelength λ (nm) was as indicated in FIG. 2.

EXAMPLE 1-2

In the case where on a substrate L_(b) having a refractive index ofn_(b5) =1.75 are formed five layers of films L₁ -L₅ made of twodifferent materials so that the refractive indexes n₁, n₂, n₃, n₄ and n₅thereof are respectively 1.39, 2.00, 1.39, 2.00, and 1.39 and that theoptical thicknesses d₁, d₂, d₃, d₄ and d₅ thereof are respectively 0.274λ_(o), 0.178 λ_(o), 0.059 λ_(o), 0.179 λ_(o) and 0.032 λ_(o), thevariation of reflectivity R(%) with wavelength λ (nm) was as indicatedin FIG. 3.

EXAMPLE 1-3

In the case where for a substrate L_(b) having a refractive index n_(b5)=1.90 two different materials were selected to form five layers of filmsL₁ -L₅ whose refractive indexes n₁, n₂, n₃, n₄ and n₅ are 1.39, 2.00,1.39, 2.00 and 1.39, respectively, and the optical thicknesses d₁, d₂,d₃, d₄ and d₅ thereof were made 0.283 λ_(o), 0.171 λ_(o), 0.042 λ_(o),0.214 λ_(o) and 0.010 λ_(o), respectively, the variation of reflectivityR(%) with wavelength λ (nm) was as indicated in FIG. 4.

EXAMPLE 1-4

For a substrate L_(b) having a refractive index 1.65, two differentmaterials were selected to form five layers of films L₁, L₂, L₃, L₄ andL₅ having refractive indexes n₁ =1.39, n₂ =2.30, n₃ =1.39, n₄ =2.30 andn₅ =1.39, respectively, and optical thicknesses d₁ =0.320 λ_(o), d₂=0.120 λ_(o), d₃ =0.125 λ_(o), d₄ =0.111 λ_(o) and d₅ =0.065 λ_(o)respectively. In this case, the variation of reflectivity R(%) withwavelength λ (nm) was as indicated in FIG. 5.

EXAMPLE 1-5

In the case of a substrate L_(b) having a refractive index of 1.75, fivelayers of films L₁, L₂, L₃, L₄ and L₅ having refractive indexes n₁=1.39, n₂ =2.30, n₃ =1.39, n₄ =2.30 and n₅ =1.39 and optical thicknessesd₁ =0.312 λ_(o), d₂ =0.133 λ_(o), d₃ =0.108 λ_(o), d₄ =0.132 λ_(o) andd₅ =0.054 λ_(o), respectively, were formed by using two differentmaterials. The resultant variation of reflectivity R(%) with wavelengthλ (nm) was as shown in FIG. 6.

EXAMPLE 1-6

In the case of a substrate L_(b) having a refractive index n_(b5) =1.90,two different materials were selected to form five layers of films L₁,L₂, L₃, L₄ and L₅ having refractive indexes n₁ =1.39, n₂ =2.30, n₃=1.39, n₄ =2.30 and n₅ =1.39 and optical thicknesses d₁ =0.294 λ_(o), d₂=0.120 λ_(o), d₃ =0.096 λ_(o), d₄ =0.130 λ_(o) and d₅ =0.040 λ_(o),respectively. The resultant variation of reflectivity R(%) withwavelength λ (nm) was as indicated in FIG. 7.

EXAMPLE 1-7

In the case where with respect to a substrate L_(b) having a refractiveindex n_(b5) =1.72 two different materials were employed to form fivelayers of films L₁, L₂, L₃, L₄ and L₅ having refractive indexes n₁=1.39, n₂ =2.10, n₃ =1.39, n₄ =2.10 and n₅ =1.39 respectively andoptical thicknesses d₁ =0.273 λ_(o), d₂ =0.200 λ_(o), d₃ =0.054 λ_(o),d₄ =0.183 λ_(o) and d₅ =0.031 λ_(o), respectively, the variation ofreflectivity (R(%) with wavelength λ (nm) was as indicated by the solidline A in FIG. 8, and is very similar to the curve B obtained bycalculation.

A second embodiment of the nonreflective coating according to thisinvention, as shown in FIG. 9, comprises seven layers of optical filmsL₁ through L₇ which, similarly as in the first embodiment, are formed onan optical substrate L_(b) such as a lens in the order opposite to thedescribed order. More specifically, the first film L₁ has a surfaceexposed to the surrounding atmosphere SA, while the lowermost or seventhfilm L₇ is deposited directly on the substrate L_(b), and the secondfilm L₂ through the sixth film L₆ are arranged between the first andseventh films L₁ and L₇. The refractive indexes of the films L₁ throughL₇ and the substrate L_(b) are designated by n₁, n₂, n₃, n₄, n₅, n₆, n₇and n_(b7), respectively, in FIG. 9.

Similarly, as in the first embodiment, the nonreflective coating is madeup of the films classified into two groups different in refractiveindex. More specifically, the first, third, fifth and seventh films L₁,L₃, L₅ and L₇ are made of a material with a low refractive index such asmagnesium fluoride MgF₂ whose refractive index is n=1.39.

The first, third, fifth and seventh films L₁, L₃, L₅ and L₇ areeffective, when the optical thicknesses d₁, d₃, d₅ and d₇ thereofsatisfy the following limitations. ##EQU3##

where λ_(o) is the light wavelength.

In addition, the optical thickness of the seventh film L₇ is determinedfrom the refractive index n_(b7) of the material of the substrate L_(b).

On the other hand, the second, fourth and sixth films L₂, L₄ and L₆ aremade of a material having a high refractive index such as zirconiumoxide ZrO₂, titanium oxide TiO₂, or cerium oxide CeO₂. Similarly as inthe above-described case, these second, fourth and sixth films L₂, L₄and L₆ are effective when the optical thicknesses d₂, d₄ and d₆ thereofsatisfy the following limitations: ##EQU4##

d₂ is substantially equal to d₄. In addition, the optical thickness d₆of the sixth film L₆ is determined essentially from the refractive indexL_(b7) of the substrate L_(b).

According to the concerned experiments, it is especially preferable inthe case of seven layers of films that the refractive index n_(b7) ofthe substrate L_(b) is in the range of from 1.45 to 1.75, i.e.1.45≦n_(b5) ≦1.75.

Now, the relationships between the film optical thicknesses and therefractive indexes in the second embodiment will be further describedwith reference to concrete examples in which the above-describedwavelength λ_(o) is employed.

EXAMPLE 2-1

In the case where for a substrate L_(b) having a refractive index n_(b7)=1.45 two different materials were selected to form seven layers offilms L₁ -L₇ whose refractive indexes n₁, n₂, n₃, n₄, n₅, n₆ and n₇ are1.39, 2.00, 1.39, 2.00, 1.39, 2.00 and 1.39 respectively, and whoseoptical thicknesses d₁, d₂, d₃, d₄, d₅, d₆ and d₇ were made 0.250 λ_(o),0.207 λ_(o), 0.029 λ_(o), 0.204 λ_(o), 0.094 λ_(o), 0.060 λ_(o) and0.076 λ_(o), respectively, the variation of reflectivity R(%) withwavelength λ (nm) was as indicated in FIG. 10.

EXAMPLE 2-2

On a substrate L_(b) having a refractive index n_(b7) =1.65, sevenlayers of films L₁ through L₇ were formed of two materials different inrefractive index, so that these films L₁ through L₇ had refractiveindexes n₁ =1.39, n₂ =2.00, n₃ =1.39, n₄ =2.00, n₅ =1.39, n₆ =2.00 andn₇ =1.39, respectively, and optical thicknesses d₁ =0.268 λ_(o), d₂=0.212 λ_(o), d₃ =0.036 λ_(o), d₄ =0.212 λ_(o), d₅ =0.090 λ_(o), d₆=0.100 λ_(o) and d₇ =0.070 λ_(o), respectively. In this case, thevariation of reflectivity R(%) with wavelength λ (nm) was as indicatedin FIG. 11.

EXAMPLE 2-3

On a substrate L_(b) having a refractive index n_(b7) =1.75, sevenlayers of films L₁ through L₂ were formed of two materials different inrefractive index so that these films had refractive indexes n₁ =1.39, n₂=2.00, n₃ =1.39, n₄ =2.00, n₅ =1.39, n₆ =2.00 and n₇ =1.39,respectively, and also optical thicknesses d₁ =0.284 λ_(o), d₂ =0.189λ_(o), d₃ =0.051 λ_(o), d₄ =0.203 λ_(o), d₅ =0.084 λ_(o), d₆ =0.121λ_(o) and d₇ =0.121 λ_(o), respectively. In this case, the variation ofreflectivity R(%) with wavelength λ (nm) was as indicated in FIG. 12.

EXAMPLE 2-4

In this example, the refractive index n_(b7) of a substrate L_(b) was1.45, and two materials different in refractive index were employed toform seven layers of films L₁ through L₇ on the substrate L_(b) as shownin FIG. 9. The refractive indexes n₁ through n₇ and optical thicknessesd₁ through d₇ of the films L₁ through L₇ were as listed below.

    ______________________________________                                        n.sub.1 = 1.39      d.sub.1 = 0.268λ.sub.o                             n.sub.2 = 2.30      d.sub.2 = 0.166λ.sub.o                             n.sub.3 = 1.39      d.sub.3 = 0.057λ.sub.o                             n.sub.4 = 2.30      d.sub.4 = 0.187λ.sub.o                             n.sub.5 = 1.39      d.sub.5 = 0.115λ.sub.o                             n.sub.6 = 2.30      d.sub.6 = 0.055λ.sub.o                             n.sub.7 = 1.39      d.sub.7 = 0.102λ.sub.o                             ______________________________________                                    

In this case, the variation of reflectivity R(%) with wavelength λ (nm)was as indicated in FIG. 13.

EXAMPLE 2-5

In this example, the refractive index n_(b7) of a substrate was 1.65,and two materials different in refractive index were employed to formseven layers of films L₁ through L₇ on the substrate L_(b) as shown inFIG. 9. The refractive indexes n₁ through n₇ and optical thicknesses d₁through d₇ of the seven films L₁ through L₇ were as listed below.

    ______________________________________                                        n.sub.1 = 1.39      d.sub.1 = 0.302λ.sub.o                             n.sub.2 = 2.30      d.sub.2 = 0.137λ.sub.o                             n.sub.3 = 1.39      d.sub.3 = 0.100λ.sub.o                             n.sub.4 = 2.30      d.sub.4 = 0.145λ.sub.o                             n.sub.5 = 1.39      d.sub.5 = 0.133λ.sub.o                             n.sub.6 = 2.30      d.sub.6 = 0.073λ.sub.o                             n.sub.7 = 1.39      d.sub.7 = 0.085λ.sub.o                             ______________________________________                                    

In this case, the variation of reflectivity R(%) with wavelength λ (nm)was as represented by the curve in FIG. 14.

EXAMPLE 2-6

Two materials different in refractive index were employed to form sevenlayers of films L₁ through L₇ on a substrate L_(b) having a refractiveindex n_(b7) =1.75. The refractive indexes n₁ through n₇ and opticalthicknesses d₁ through d₇ of the films L₁ through L₇ were as listedbelow.

    ______________________________________                                        n.sub.1 = 1.39      d.sub.1 = 0.270λ.sub.o                             n.sub.2 = 2.30      d.sub.2 = 0.164λ.sub.o                             n.sub.3 = 1.39      d.sub.3 = 0.059λ.sub.o                             n.sub.4 = 2.30      d.sub.4 = 0.198λ.sub.o                             n.sub.5 = 1.39      d.sub.5 = 0.102λ.sub.o                             n.sub.6 = 2.30      d.sub.6 = 0.091λ.sub.o                             n.sub.7 = 1.39      d.sub.7 = 0.077λ.sub.o                             ______________________________________                                    

In this example, the variation of reflectivity R(%) with wavelength λ(nm) was as indicated in FIG. 15.

EXAMPLE 2-7

In this example also, two materials different in refractive index wereemployed to form seven layers of films L₁ through L₇ on a substrateL_(b) having a refractive index n_(b7) =1.75, as shown in FIG. 9. Therefractive indexes n₁ through n₇ and optical thicknesses d₁ through d₇of the films L₁ through L₇ were as listed below:

    ______________________________________                                        n.sub.1 = 1.39      d.sub.1 = 0.268λ.sub.o                             n.sub.2 = 2.10      d.sub.2 = 0.188λ.sub.o                             n.sub.3 = 1.39      d.sub.3 = 0.046λ.sub.o                             n.sub.4 = 2.10      d.sub.4 = 0.200λ.sub.o                             n.sub.5 = 1.39      d.sub.5 = 0.104λ.sub.o                             n.sub.6 = 2.10      d.sub.6 = 0.072λ.sub.o                             n.sub.7 = 1.39      d.sub.7 = 0.082λ.sub.o                             ______________________________________                                    

In this case, the variation of reflectivity R(%) with wavelength λ (nm)was as indicated by the curve A in FIG. 16. This curve A is very similarto the curve B obtained by calculation.

In the above-described examples, all of the films having a higherrefractive index are less than 100 nm in thickness. According to theexperiments, it has been found that with the film thickness of thisorder, no nonuniformity in refractive index is caused. Therefore, it ispreferable that the nonreflective coating is made as described above, inorder to eliminate the difficulties (3), (4) and (5) accompanying theconventional nonreflective coating. During the formation of the filmshaving the thicknesses as described above by vacuum evaporation, nointroduction of gas is required, and accordingly strong films can beformed by vacuum evaporation at a sufficiently high degree of vacuum.

As is apparent from the above description, the thicknesses of five orseven layers of films are so designed that the nonreflective coatingmade up of these films is applicable to a substrate whose refractiveindex is within a wide refractive index range. Furthermore, the filmsare formed of a relatively small number of materials different inrefractive index. Thus, the nonreflective coating according to thisinvention shows an excellent reflection preventing effect over a widerange of light wavelengths.

What is claimed is:
 1. A multi-layer nonreflective optical coating on anoptical substrate, comprising: five optical film layers, respectivelycomprised of a first material having a first index of refraction and asecond material having a second index of refraction higher than saidfirst index of refraction, superposed and disposed in contact in thefollowing order;a first layer of the first material having an opticalthickness d₁, wherein 0.270λ≦d₁ ≦0.320λ; a second layer of the secondmaterial having an optical thickness d₂, wherein 0.120λ≦d₂ ≦0.210λ; athird layer of the first material having an optical thickness of d₃,wherein 0.042λ≦d₃ ≦0.125λ; a fourth layer of the second material havingan optical thickness d₄, wherein 0.111λ≦d₄ ≦0.214λ, wherein said secondand fourth layers have substantially the same optical thickness; a fifthlayer of the first material having an optical thickness d₅, wherein0.010λ≦d₅ ≦0.065λ; and an optical substrate having an index ofrefraction of from 1.65 to 1.90 at light wavelength λ, and having saidfive contacting superposed optical film layers disposed thereon withsaid fifth layer contacting said substrate.
 2. A multi-layernonreflective optical coating on an optical substrate, comprising: sevenoptical film layers, respectively comprised of a first material having afirst index of refraction and a second material having a second index ofrefraction higher than said first index of refraction, superposed anddisposed in contact in the following order;a first layer of the firstmaterial having an optical thickness d₁, wherein 0.250λ≦d₁ ≦0.302λ; asecond layer of the second material having an optical thickness d₂,wherein 0.137λ≦d₂ ≦0.212λ; a third layer of the first material having anoptical thickness d₃, wherein 0.029λ≦d₃ ≦0.100λ; a fourth layer of thesecond material having an optical thickness d₄, wherein 0.145λ≦d₄≦0.212λ, wherein said second and fourth layers have substantially thesame optical thickness; a fifth layer of the first material having anoptical thickness d₅, wherein 0.084λ≦d₅ ≦0.133λ; a sixth layer of thesecond material having an optical thickness d₆, wherein 0.055λ≦d₆≦0.121λ; a seventh layer of the first material having an opticalthickness d₇, wherein 0.070λ≦d₇ ≦0.121λ; and an optical substrate havingan index of refraction of from 1.45 to 1.75 at light wavelength λ, andhaving said seven contacting superposed optical film layers disposedthereon with said seventh layer contacting said substrate.